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Journal Article

Kasner-like behaviour for subcritical Einstein-matter systems


Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Damour, T., Henneaux, M., Rendall, A. D., & Weaver, M. (2002). Kasner-like behaviour for subcritical Einstein-matter systems. Annales Henri Poincare, (3), 1049-1111.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-543A-0
Confirming previous heuristic analyses \''a la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain ''''subcritical Einstein-matter systems exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike singularity. The D-dimensional coupled Einstein-dilaton-p-form system is subcritical if the dilaton couplings of the p-forms belong to some dimension dependent open neighbourhood of zero, while pure gravity is subcritical if D is greater than or equal to 11. Our proof relies, like the recent theorem dealing with the (always subcritical) Einstein-dilaton system, on the use of Fuchsian techniques, which enable one to construct local, analytic solutions to the full set of equations of motion. The solutions constructed are ''''general in the sense that they depend on the maximal expected number of freefunctions.